There were two men by that name in the 3rd US Colored Cavalry:

According to the Company Descriptive Books:

1. William Sims, age 24, 5' 6", farmer, born in Warren County, enlisted in Company A at Vicksburg, Oct. 5, 1863.

2. William Sims, age 25, 5' 6", laborer, born in Claiborne County, enlisted in Company M at Vicksburg, Oct. 27, 1864.